An Equivalent Hermitian Hamiltonian for the non-Hermitian -x^4 Potential

The potential -x^4, which is unbounded below on the real line, can give rise to a well-posed bound state problem when x is taken on a contour in the lower-half complex plane. It is then PT-symmetric rather than Hermitian. Nonetheless it has been shown numerically to have a real spectrum, and a proof of reality, involving the correspondence between ordinary differential equations and integral systems, was subsequently constructed for the general class of potentials -(ix)^N. For PT-symmetric but non-Hermitian Hamiltonians the natural PT metric is not positive definite, but a dynamically-defined positive-definite metric can be defined, depending on an operator Q. Further, with the help of this operator an equivalent Hermitian Hamiltonian h can be constructed. This programme has been carried out exactly for a few soluble models, and the first few terms of a perturbative expansion have been found for the potential m^2x^2+igx^3. However, until now, the -x^4 potential has proved intractable. In the present paper we give explicit, closed-form expressions for Q and h, which are made possible by a particular parametrization of the contour in the complex plane on which the problem is defined. This constitutes an explicit proof of the reality of the spectrum. The resulting equivalent Hamiltonian has a potential with a positive quartic term together with a linear term.Comment: New reference [10] added and discussed. Minor typographical correction

CSM docked DAP/orbital assembly bending interaction-axial case

A digital autopilot which can provide attitude control for the entire Skylab orbital assembly using the service module reaction control jets is described. An important consideration is the potential interaction of the control system with the bending modes of the orbital assembly. Two aspects of this potential interaction were considered. The first was the possibility that bending induced rotations feeding back through the attitude sensor into the control system could produce an instability or self-sustained oscillation. The second was whether the jet activity commanded by the control system could produce excessive loads at any of the critical load points of the orbital assembly. Both aspects were studied by using analytic techniques and by running simulations on the all-digital simulator

A process model of children's early verb use

The verb-island hypothesis (Tomasello, 1992) states that children’s early grammars consist of sets of lexically-specific predicate structures (or verb-islands). However, Pine, Lieven and Rowland (1998) have found that children’s early language can also be built around lexical items other than verbs, such as pronouns (this contradicts a strict version of the verb-island hypothesis). This paper presents a computational model (called MOSAIC), which constructs a network of nodes and links based on a performance-limited distributional analysis of the input (mother’s speech). The results show that utterances generated from MOSAIC: (1) more closely resemble the child’s data than the child’s mother’s data on which MOSAIC is trained; and (2) can readily simulate both the verb-island and other-island phenomena which exist in the child’s data

Learning novel sound patterns

The acquisition of vocabulary represents a key phenomenon in language acquisition, yet it is still poorly understood. Gathercole and colleagues have recently provided a rigorous test of vocabulary knowledge (the nonword repetition test, Gathercole, Willis, Baddeley, & Emslie, 1994) and have adapted the phonological loop part of the working memory model (Baddeley & Hitch, 1974) to explain the nonword repetition findings (e.g. Gathercole & Baddeley, 1989). However, there are two major failings in their explanation: there is no description of how words are learned, and no definition of how the phonological loop interacts with long-term memory. We present an EPAM based computational model which overcomes these problems by combining the phonological loop approach with the EPAM/chunking approach (Feigenbaum & Simon, 1984). Trained on naturalistic phonemically coded speech (from mother’s utterances to 2-3 year old children), the model provides a good match to the nonword repetition data from 2-3 year old children. The model is also able to show the effect on nonword repetition when the model is trained using different sets of input. Implementing the phonological loop within EPAM represents a parsimonious approach to learning novel sound patterns and provides a more precise definition of how vocabulary acquisition may occur

State-of-the-art of turbofan engine noise control

The technology of turbofan engine noise reduction is surveyed. Specific topics discussed include: (1) new fans for low noise; (2) fan and core noise suppression; (3) turbomachinery noise sources; and (4) a new program for improving static noise testing of fans and engines

Cosmic ray diffusion: Report of the Workshop in Cosmic Ray Diffusion Theory

A workshop in cosmic ray diffusion theory was held at Goddard Space Flight Center on May 16-17, 1974. Topics discussed and summarized are: (1) cosmic ray measurements as related to diffusion theory; (2) quasi-linear theory, nonlinear theory, and computer simulation of cosmic ray pitch-angle diffusion; and (3) magnetic field fluctuation measurements as related to diffusion theory

Fracture behavior of unidirectional boron/aluminum composite laminates

An experiment was conducted to verify the results of mathematical models which predict the stresses and displacements of fibers and the amount of damage growth in a center-notched lamina as a function of the applied remote stress and the matrix and fiber material properties. A brittle lacquer coating was used to detect the yielding in the matrix while X-ray techniques were used to determine the number of broken fibers in the laminate. The notched strengths and the amounts of damage found in the specimens agree well with those predicted by the mathematical model. It is shown that the amount of damage and the crack opening displacement does not depend strongly on the number of plies in the laminate for a given notch width. By heat-treating certain laminates to increase the yield stress of the alumina matrix, the effect of different matrix properties on the fracture behavior was investigated. The stronger matrix is shown to weaken the notched laminate by decreasing the amount of matrix damage, thereby making the laminate more notch sensitive

Quasi-linear theory via the cumulant expansion approach

The cumulant expansion technique of Kubo was used to derive an intergro-differential equation for f , the average one particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the f equation degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory for this limited class of fluctuations. For more physically realistic fluctuations, however, quasi-linear theory is at best approximate

A magnetic thrust action on small bodies orbiting a pulsar

We investigate the electromagnetic interaction of a relativistic stellar wind with small bodies in orbit around the star. Based on our work on the theory of Alfv\'en wings to relativistic winds presented in a companion paper, we estimate the force exerted by the associated current system on orbiting bodies and evaluate the resulting orbital drift. This Alfv\'enic structure is found to have no significant influence on planets or smaller bodies orbiting a millisecond pulsar. %influence on the orbit of bodies around a millisecond pulsar. On the timescale of millions of years, it can however affect the orbit of bodies with a diameter of 100 kilometres around standard pulsars with a period $P \sim$1 s and a magnetic field $B \sim 10^{8}$ T. Kilometer-sized bodies experience drastic orbital changes on a timescale of $10^4$ years.Comment: accepted for publication in "Astronomy and Astrophysics